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Supervisory Framework for Risk Assessment and Risk-based Solvency

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Global Regulatory Tendencies There are costs and risks to a program of action, but they are far less than the long-range risks and costs of comfortable inaction John F. Kennedy In the past, insurance supervisors but also insurance companies were not sufficiently aware of economic reality • The valuation of assets and liabilities were not adequate for an analysis of risk • The artificial smoothing of results often made companies and supervisors inclined to comfortable inaction • An adequate risk quantification was perceived by some to be too complex and too onerous The financial crisis of 2000/2001 has shown to all that the insurance industry was more exposed than previously thought and both insurers and regulators saw the need for a more adequate, risk based supervisory framework  many regulators (UK, NL, CH,…) and the EU have started initiatives to develop more risk based supervisory models

Prudential Supervision Prudential Supervision aims to systematically evaluate the risk profile and the risk bearing capacity of the supervised entities. Finnish Financial Supervisory Authority What prudential supervision is about is helping protect other people from the failure of the institution by trying to ensure the institution is adequately run. An adequately-run institution needs to know why it’s in business. It need s to have a strategy and some idea of where its revenues will come from. It needs to know what kind of risks it faces and, preferably, to try to measure them. It needs to know what kinds of risks it wants to face and take measures to eliminate the rest. And it needs to have some way of telling how much capital it needs to deliver an acceptable risk-adjusted return to shareholders Howard Davis, Chairman, Financial Services Authority, UK Prudential supervision is not only about quantifying insurers’ risks, but to give incentives so that the companies themselves manage their risks appropriately, i.e. have an adequate risk management and corporate governance

Risk Management Wir müssen wissen. Wir werden wissen. David Hilbert Risk management is responsible for identifying, assessing, analyzing, quantifying and then transferring, mitigating or accepting of risk For risk management to be effective, there needs to be a risk culture such that senior management wants to know and risk management is able to tell the “truth” about the risks Senior management and the board have to ensure that there is a honest dialog and transparency regarding risks within the company Risk management is not solely about control but about confronting issues and uncomfortable truths openly and honestly A risk based supervisory framework should be such that it fosters a climate in the market where an appropriate risk culture and risk management is rewarded  principles instead of rules  responsibility with senior management  transparency and trust in market and in regulator

Risk Management Warren Buffett‘s three key principles for running a successful insurance business: • They accept only those risks that they are able to properly evaluate (staying within their circle of competence) and that, after they have evaluated all relevant factors including remote loss scenarios, carry the expectancy of profit. These insurers ignore market-share considerations and are sanguine about losing business to competitors that are offering foolish prices or policy conditions. • They limit the business they accept in a manner that guarantees they will suffer no aggregation of losses from a single event or from related events that will threaten their solvency. They ceaselessly search for possible correlation among seemingly-unrelated risks. • They avoid business involving moral risk: No matter what the rate, trying to write good contracts with bad people doesn't work. While most policyholders and clients are honorable and ethical, doing business with the few exceptions is usually expensive, sometimes extraordinarily so. February 28, 2002, Warren E. Buffett • An insurance regulator should set incentives such, that good risk management practices are rewarded: • setting transparent requirements • putting responsibility to the board and senior management • Enforce requirements consistently

Prudential Supervision: Pitfalls to Avoid A regulator has to be careful not to give incentives for secondary risk management of supervisors Secondary Risk Management: the preoccupation of risk managers with managing their own risks. This can lead to a culture of risk aversion. Symptoms are that disclaimer paragraphs become longer than the expert opinion, a proliferation of risks which are considered in order to be able to cover all bases, the perception that all risk are unacceptable and a preoccupation with residual, ill-defined risk. (based on ‘The Risk Management of Everything: Rethinking the politics of uncertainty’, Michael Power, Demos 2004) • Symptoms of secondary risk management in supervision: • The insistence on limits on investments and products • The fear of transparency, allowing comfortable inaction • An obsession with formalities rather than substance • The fear and rejection of all things new and unconventional Secondary risk management has to be fought with transparency: of the economic state of the companies but also of the regulatory requirements and a continuing, public engagement of the supervisors with all stakeholders

Prudential Supervision: Pitfalls to Avoid Risk management is crucial, however, there are some pitfalls to avoid The Regulation of Everything Regulation should concentrate on relevant risks Self-regulation and market forces should have their place The Myth of Auditability Audits should not be used to abrogate responsibility Over-reliance on auditability can lead to check-box mentality both within the industry and the regulator Limits of Quantification Residual risks (e.g. operational risks) can become blown up all out of proportion Due to lack of data and clear concepts, pseudo-quantifications are used for capital requirements Dangers of Secondary Risk Management Excessive reflection on risks can lead to the perception that danger lurks everywhere Risk management should deal with a company‘s risks, not manage their own risk Excessive Internal Control Excessive internal control can lead to a bureaucratic, risk averse company

Principles vs Rules for Risk-Based Solvency Principle-based standards describe the objective sought in general terms and require interpretation according to the circumstance. Companies tailor approach such that clearly stated objective is attained Objective can be attained if companies interpret principles faithfully Principle-based Objective Company specific risk-based solvency assessment = Rule-based Objective Rule based approach does not allow truly company specific risk assessment (or the set of rules becomes huge and Byzantine) Attained result deviates from true company specific solvency requirement, depending on how well rules capture the situation of the insurer

Capital Models • Most capital models and solvency models consist of two main parts: • A valuation V(.) is a mapping from the space of financial instruments (assets and liabilities) in R: • V: A * L  R, where A * L is the space of all assets and liabilities • A risk measure rm(.) of a random variable: rm: G R Necessary capital C for risk is quantified by the risk measure of the change of risk bearing capital over a given time horizon (e.g. 1 year) Risk bearing capital is defined as value of assets V(A) less value of liabilities V(L), where value is generally market value. Let RBC(k)=V(A(k))-V(L(k)) be the risk bearing capital at time k. Then The mathematical set up is slightly different for multiperiod models C=rm( RBC(t) – RBC(0) ) Risk bearing capital at time t: random variable Risk bearing capital at time 0: known

Capital Models • An economic capital model should be consistent • between valuation and risk quantification and • between the valuationofassets and valuation ofliabilities Often V1(.): A R and V2(l): L R are used i.e. the valuation of assets and liabilities are different functionals, which are not necessarily consistent. • Examples: • Solvency 1: V1(.) is a mix of market value and book-values, V2 is basically unspecified (undiscounted, prudent etc.) • Solvency 2: V1(.) is market value, V2(.) is discussed to be 90% quantile of the ultimate of the liabilities • SST: V1(.) is market value, V2(.) is best estimate + cost for of future regulatory capital Consistency requirement for valuation: If a ~ l, a in A, l in L, then V(a)  V(l) Bad example: A pure endowment insurance is close to a ZCB. However, the market value of a ZCB can be far away from its statutory value

Risk Based Solvency Frameworks There are some unique challenges when developing regulatory capital models: • They need to be applicable to a wide range of companies • They should be flexible in order to allow adaptation to new risks • They should be close to companies’ internal models • Their underlying principles should be transparent • They should be easily recalibrated if risk factors change (e.g. financial market risk) • They should not be so complex as to inhibit use of internal models • They should not be so simple as to not allow the use of partial model as a stepping stone for smaller companies to full internal models The art of defining a regulatory capital model is to find an optimal solution fitted to the specific insurance market

Scope of Regulatory Models Subsidiaries: Can be in all parts of the world, home country regulator cannot calibrate easily (if at all) a standard model to different risk profiles. Mix of legal entity risk to risks emanating from subsidiaries is widely varying from group to group. Capital flow between subsidiaries and parent is restricted. Risk specific standard model for group is extremely difficult to develop since in addition to legal entity model restrictions on fungibility of capital need to be taken into account Group Subsidiary Subsidiary Subsidiary Parent Company: Standard model can be calibrated using local, country specific statistics and models Legal Entity Branch Branch Parent Company Risk specific standard model for legal entity is very difficult to develop Risk specific standard model is feasible Branch Branch Branches: Can be in all parts of the world, home country regulator cannot calibrate easily (if at all) a standard model to different risk profile. Mix of parent country risk to risks emanating from branches is widely varying from company to company Capital can flow (nearly) freely between branches and parent company and legal entity can be considered to be one risk-entity. Diversification between parent and branches.

RBC Forbidden states SCR t=0 t=T Time Horizon The time horizon of 1 year used by most internal models and supervisory frameworks is not natural but a compromise: • A time horizon of one year is short enough that asset and business strategy need not necessarily be modeled: assume that asset and liability composition at the end of one year is more or less as at the beginning of the year • Since solvability requirements (in theory) have to be fulfilled at each point in time a time horizon of one year is short enough so that satisfying the solvency requirement only at the end of each year is a reasonable approximation to a continuous model • However, the are also disadvantages to a one year time horizon: • Diversification over time is limited • During one year many things can happen (strategies can change, assets rebalanced etc.  SST requires to do a recalculation if risk situation has changed substantially

Risk Risk: In the abstract, used to indicate a condition of the real world in which there is a possibility of loss; also used by insurance practitioners to indicate the property insured or the peril insured against. IAIS Glossary of Terms An investor‘s initial portfolio consists of positions Ai, 1≤i≤I, (possibly with some institutional constraints such as the absence of short sales and a „congruence“ for each currency between assets and liabilities). The position Ai provides Ai(T) units of currency i at date T. We call risk the investor‘s future net worth sum ei*Ai(T) (ei denotes the random number of units of currency 1 which one unit currency i buys at time T.) Coherent Measures of Risk, Artzner, Delbaen, Eber, Heath Risk is the chance of something happening that will have an impact upon objectives. It is measured in terms of consequences and likelihood. Australian and New Zealand Standard on Risk Management

Risk Measures: Expected Shortfall vs VaR The Expected Shortfall of a random variable X to the confidence level 1- (ES) is given by ES[X] =1/α · E[ max( X- VaR[X], 0 )] + VaR[X] Expected Shortfall is a coherent risk measure Shareholder: Only default or non-default is relevant not how bad the state of the insurer is in case of default as shareholders have a put-option on the insurer (Merton)  Value-at-Risk might be appropriate Policy Holder: In case of default, it matters how much capital is left  Expected Shortfall is more appropriate than VAR • From the perspective of an insurance regulator, Expected Shortfall has advantages compared to Value at Risk • For an insurer, Expected Shortfall has advantage of being coherent: • Allocation of risk and risk management of subunits is possible • ES is easier to explain to management: • ES1%=average one-in-a-hundred-years loss • VaR1% = the loss that is in 99-out-of-a-100-years not exceeded

Valuation: The economic view How to measure risks? • Accounting risk or economic risk? Reported earnings follow the rules and principles of accounting. The results do not always create measures consistent with underlying economics. However, corporate management’s performance is generally measured by accounting income, not underlying economics. Therefore, risk management strategies are directed at accounting, rather than economic performance. Enron in-house risk-management handbook For a risk-based solvency system, risks need to be measured objectively and consistently → economic risk rather than accounting risk →Market Consistent Valuation of Assets and Liabilities

Valuation: Market Value vs. Amortized Cost • Economic Consequences of Amortized Cost: • Amortized cost only makes (marginally) sense when bonds are truly held to maturity, but then: • investment opportunities vanish • if market value of bonds is below amortized cost, any selling of a bond leads to realization of a loss • if assets have to be sold, recently bought bonds or equities have to be used to keep realized losses under control • if business decreases, cash outflow might have to be served by bonds, leading to a realization of losses • In an amortized cost world, companies have an incentive to write loss making business in order not to be forced to sell bonds, exacerbating thereby underwriting cycles, in particular when interest rates rise • In addition, the amortized cost framework is difficult – if not impossible – to extend to derivatives, making it impossible to take into account sophisticated hedging strategies • If a company becomes insolvent, the portfolio cannot be sold to second insurer if economic worth of the company is negative under market consistent valuation even if under an amortized cost the valuation looks fine Amortized cost framework for assets gives incentives for perverse risk management: • Foreclosing of investment opportunities • Cash flow underwriting • Downward spiral when business contracts Amortized cost framework for assets is difficult to extend to derivatives and more complex instruments

Market Value Margin • Asset valuation: Market consistent • Market price if traded • Marked to Model if not traded Liability valuation: How to define if liability valuation has to be consistent with asset valuation? Problem: Most liabilities are not actively traded  Marked to Model Asset Valuation: Fair Value = the price at which an asset or liability could be exchanged in a current transaction between knowledgeable, unrelated willing parties. The price is an estimate in the absence of an actual exchange(FASB) At what price could an insurance liability be transferred to a willing buyer (e.g. to an insurer)? Definition:The market value margin is the smallest amount which is necessary in addition to the best-estimate of the liabilities, so that a buyer would be willing to take over the portfolio of assets and liabilities.

Market Value Margin: Cost of Capital Approx. What is a good proxy for the Market Value Margin? Proposals: Quantile and Cost of Capital Approach Idea: A buyer (or a run-off company) needs to put up regulatory capital during the run-off period of the portfolio of assets and liabilities  a potential buyer needs to be compensated for the cost of having to put up regulatory capital Market Value Margin = the present value of future regulatory risk capital costs associated with the portfolio of assets and liabilities Problem: How to determine future regulatory capital requirement during the run-off of the portfolio of assets and liabilities?

Market Value Margin: Cost of Capital Approx. Risks considered in the MVM: t=0 t=1 t=2 t=3 Years Risks emanating during year 2 are covered by the cost of setting up SCR(2): CoC*SCR(2) compensates for having to finance SCR(2) during one year Risks emanating during year 1 are covered by the cost of setting up SCR(1): CoC*SCR(1) compensates for having to finance SCR(1) during one year Risks emanating during year 0 are covered by the SCR(0) Note: This approach for calculation the cost of capital margin assumes that the portfolio transfer occurs at the end of year 0, hence SCR(0) does not enter calculation

Market Value Margin: Cost of Capital Approx. Calculation of the Cost of Capital Margin: 1. calculate the capital requirement SCR(t) for all years t until the run-off of the portfolio, assuming no new business and assume that asset portfolio equals to optimal replicating portfolio (i.e. only unhedgeable risks remain for SCR(t)). 2. calculate the capital charge, i.e. the cost of holding the required capital, for each projection year as the required amount of capital multiplied by a cost of capital. 3. the cost of capital margin is then determined as the present value of the (discounted) capital charges as projected over the full time horizon of the liabilities Step 1 is the difficult one. In theory, one needs to do a full solvency test for each year until the portfolio has run-off. In practice simplifications can be employed • Determine a proxy p(t) for future SCR(t) which is easier to calculate than SCR(t), i.e. the best-estimate of liabilities at time t. • Then approximate SCR(t) using the proxy p(t). • Show to the supervisor that the proxy is reasonable

Market Value Margin: Cost of Capital Approx. Example: • Assume that the best estimate of liabilities BE(t) is a good proxy for future SCR(t) • Determine SCR(0) without current year risk (premium risk) and assume assets are optimal replicating liabilities  only unhedgeable financial market risk needs to be considered. • Call this value: SCR(0)’ • Then set SCR(t)=SCR(0)’/BE(0)*BE(t), t=1,…,T SCR(3)=SCR(0)/BE(0)*BE(3)=20/200*7=7

Market Consistent Valuation: Definition • Advantages of the Cost of Capital Margin Approach: • The CoCM is defined as a proxy for the MVM, therefore it fits into a market consistent valuation framework • It can be defined consistently for both life and P&C companies • It allows a range of calculation methods, from very sophisticated to simplified • It is congruent to the margins used by many companies internally (e.g. for pricing, for EEV,…) • It forces companies to think about long term risk and capital requirements • For supervisors, the CoCM is easy to review

Economic Balance Sheet Building blocks: Market consistent (economic) balance sheet Free capital Risk bearing capital SCR: Required capital for 1-year risk Target capital Market value of assets Market Value Margin Wherever possible, market-consistent valuation is based on observable market prices (marking to market) If such values are not available, a market-consistent value is determined by examining comparable market values, taking account of liquidity and other product-specific features, or on a model basis (marking to model) Market-consistent means that up to date values are used for all parameters Market consistent value of liabilities Best estimate of liabilities Best-estimate = Expected value of liabilities, taking into account all up to date information from financial market and from insurance. All relevant options and guarantees have to be valued. No explicit or implicit margins Discounting with risk-free interest rate

Risk as Change of Risk Bearing Capital Building blocks: Year 0 Year 1 Probability density of the change of risk bearing capital Risk bearing capital Revaluation of liabilities due to new information Market Value Margin Probability < 1% New business during one year Claims Change in market value of assets Average value of RBC in the 1% ‚bad‘ cases = Expected Shortfall = SCR Catastrophes Market consistent value of liabilities Smallest value of RBC in the 1% ‚bad‘ cases = Value at Risk Market value of assets Best estimate of liabilities Economic balance sheet at t=0 (deterministic) Economic balance sheet at t=1 (stochastic)

Outlook • There have been great improvements in risk based solvency frameworks during the last years, many problems however are still unsolved • A regulator developing a risk based solvency framework should have in view not only the current knowledge and modeling capabilities but should base the framework on what will be available in a few years time • Risk-based solvency systems will co-evolve with insurance market • There is not one best risk based solvency system, but mix of rules and principle, level of sophistication etc. depends on the ‘culture’ of the market • One should never forget that the point of a risk based solvency system is not only the calculation of target capital (or SCR) but to foster a risk awareness in the market (and in the regulator)

The SST Concept: Requirements • Transparent methodology • The model should correspond to the ideas of the users • Easy to adjust to changing risk landscape • Easy integration of internal models • To give incentives for risk management • As simple as possibly, as complex as necessary SST models and all parameters are published and are in the ‚public domain‘ SST is modular, partial modules can easily be changed or improved Calculation is responsibility of management, SST is clear and understandable for management Not a simple factor model but a model which needs to be adapted by each insurer to its specific situation

The SST Concept: Principle-Based Core of the Solvency Test Principles Definitions Glossary Guidelines Standard Model The SST is defined not by the Standard Model but by underlying principles • Principles define concisely the desired objectives • Definition of terms and concepts so that meaning and possible interpretation of principles become clear • Glossary with terms and concepts • Guidelines help in interpretation • Standard Model allows use of Solvency Test also by small companies

The SST Concept: Principle-Based • All assets and liabilities are valued market consistently • Risks considered are market, credit and insurance risks • Risk-bearing capital is defined as the difference of the market consistent value of assets less the market consistent value of liabilities, plus the market value margin • Target capital is defined as the sum of the Expected Shortfall of change of risk-bearing capital within one year at the 99% confidence level plus the market value margin • The market value margin is approximated by the cost of the present value of future required regulatory capital for the run-off of the portfolio of assets and liabilities • Under the SST, an insurer’s capital adequacy is defined if its target capital is less than its risk bearing capital • The scope of SST is legal entity and group / conglomerate level domiciled in Switzerland • Scenarios defined by the regulator as well as company specific scenarios have to be evaluated and, if relevant, aggregated within the target capital calculation Defines Output

The SST Concept: Principle-Based • All relevant probabilistic states have to be modeled probabilistically • Partial and full internal models can and should be used. If the SST standard model is not applicable, then a partial or full internal model has to be used • The internal model has to be integrated into the core processes within the company • SST Report to supervisor such that a knowledgeable 3rd party can understand the results • Disclosure of methodology of internal model such that a knowledgeable 3rd party can get a reasonably good impression on methodology and design decisions • Senior Management is responsible for adherence to principles Defines How-to Transpar-ency Responsi-bility

The SST Concept: Standard Models • Financial Market Risk • For many companies this is the most important risk (up to 80% of total target capital emanating from financial market risk) • Most relevant are interest rate risk, real estate risk, spread risk, equity risk • Financial market risk model does take into account assets and liabilities simultaneously • Interest rate risk is captured not via simple duration but over different (13) time buckets • Credit Risk • Credit risk is becoming more important as companies go out of equity and into corporate bonds • Many smaller and mid-sized companies do not yet have much experience in modeling credit risk • Insurance Risk (Life) • For many life companies with predominantly savings product, pure life insurance risk is not too important • Life insurance risk is substantial for companies selling more risk products / disability • Model needs to capture optionalities and policyholder behavior • Insurance Risk (Nonlife) • Premium-, reserving- and cat risk are important • A broad consensus on modeling exists among actuaries More information under: www.sav-ausbildung.ch and www.bpv.admin.ch